The inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic: an unbiased estimator in the presence of independent censoring

The win ratio method has received much attention in methodological research, ad hoc analyses, and designs of prospective studies. As the primary analysis, it supported the approval of tafamidis for the treatment of cardiomyopathy to reduce cardiovascular mortality and cardiovascular-related hospitalization. However, its dependence on censoring is a potential shortcoming. In this article, we propose the inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic (i.e., the IPCW-adjusted win ratio statistic) to overcome censoring issues. We consider independent censoring, common censoring across endpoints, and right censoring. We develop an asymptotic variance estimator for the logarithm of the IPCW-adjusted win ratio statistic and evaluate it via simulation. Our simulation studies show that, as the amount of censoring increases, the unadjusted win proportions may decrease greatly. Consequently, the bias of the unadjusted win ratio estimate may increase greatly, producing either an overestimate or an underestimate. We demonstrate theoretically and through simulation that the IPCW-adjusted win ratio statistic gives an unbiased estimate of treatment effect.赢比法（win ratio method）在方法学研究、特设分析及前瞻性研究设计中广受关注。作为核心分析手段，它曾助力他法米迪（tafamidis）获批用于心肌病治疗，以降低心血管死亡率与心血管相关住院风险。不过，该方法对截尾（censoring）的依赖是其潜在短板。本文提出了逆概率截尾加权（inverse-probability-of-censoring weighting, IPCW）校正赢比统计量（即IPCW校正赢比统计量）以解决截尾相关问题。我们考虑了独立截尾、终点共用截尾及右截尾三种场景，推导了IPCW校正赢比统计量对数形式的渐近方差估计量，并通过模拟实验对其性能进行评估。模拟研究结果显示，随着截尾比例升高，未校正赢比例会大幅降低，进而导致未校正赢比估计的偏差显著增大，可能出现高估或低估的结果。本文通过理论推导与模拟实验证实，IPCW校正赢比统计量能够得到治疗效应的无偏估计。